Question: A circle has a sector with area $6\pi$ and central angle $135^\circ$. What is the area of the circle? ${16\pi}$ $\color{#9D38BD}{135^\circ}$ ${6\pi}$
The ratio between the sector's central angle $\theta$ and $360^\circ$ is equal to the ratio between the sector's area, $A_s$ , and the whole circle's area, $A_c$ $\dfrac{\theta}{360^\circ} = \dfrac{A_s}{A_c}$ $\dfrac{135^\circ}{360^\circ} = 6\pi \div A_c$ $\dfrac{3}{8} = 6\pi \div A_c$ $A_c \times \dfrac{3}{8} = 6\pi$ $A_c = 6\pi \times \dfrac{8}{3}$ $A_c = 16\pi$